Let {at}tez be xt = 1xt-1+ at, te Z where at ~ WN(0, 0²) and 1 € (−1, 1) is a fixed parameter, whence xt is a stationary process. (a) Derive the mean function t = Ext for t = Z. (b) Derive the autocovariance function Yt,t+h = Cov(xt, xt+h) for t, h = Z. (c) For ₁ € (-1, 1), derive the autocorrelation function (ACF) Pt,t+h = Cor(t, xt+h) for t, h = Z. Describe the shape of the ACF.

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